As your dynamic part is surrounded by two static part you can use them to find it.
\\profile\\(.*)\\details
Now if you want to replace only the middle part you can either use LookAround.
string pattern = @"(?<=\\profile\\).*(?=\\details)";
string substitution = @"titi";
string input = @"\profile\name\details
\profile\name\details
";
RegexOptions options = RegexOptions.Multiline;
Regex regex = new Regex(pattern, options);
string result = regex.Replace(input, substitution);
Or use the replacement patterns $
GroupIndex
string pattern = @"(\\profile\\)(.*)(\\details)";
string substitution = @"$1Replacement$3";
string input = @"\profile\name\details
\profile\name\details
";
RegexOptions options = RegexOptions.Multiline;
Regex regex = new Regex(pattern, options);
string result = regex.Replace(input, substitution);
For readable nammed group substitution is a possibility.